Non-commutative Algebra

Code:

M561

Acronym:

M561

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	3	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

The aim of this course is to introduce the students to some aspect of non-commutative (associative) algebras and their modules. Starting from skew-fields we will pass to separable algebras and arbitrary Hopf algebras, going further into depth by discussing some of the classification results for finite dimensional Hopf algebras and some recent constructions for infinite dimensional Hopf algebras.

Learning outcomes and competences

The expected outcome is that the student knows some of the recent trends in the theory of (finite or infinite dimensional) Hopf algebra.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Linear Algebra and basic abstract algebra, including basic facts on groups, rings and modules.

Program

The syllabus will roughly be as follows:

1. Brauer group


2. Separable extensions


3. Frobenius extensions


4. Finite dimensional Hopf algebras




1. Semisimple Hopf algebras


2. Pointed Hopf algebras




5. Infinite dimensional Hopf algebras




1. Quantized enveloping algebras


2. Ore extensions as Hopf algebras

Mandatory literature

H.J. Schneider; Lectures on Hopf algebras, 1994 (http://www.famaf.unc.edu.ar/andrus/papers/Schn1.pdf)
Sweedler Moss E.; Hopf algebras. ISBN: 8053-9255-6
Susan Montgomery; Hopf algebras and their actions on rings, AMS, 1993. ISBN: 978-0-8218-0738-5 (https://link.springer.com/book/10.1007/978-0-387-72766-0)

Complementary Bibliography

Dascalescu Sorin; Hopf algebras. ISBN: 0-8247-0481-9
Abe Eiichi; Hopf algebras. ISBN: 0-521-22240-0
Caenepeel Stefaan; Brauer groups, Hopf algebras and Galois theory. ISBN: 0-7923-4829-X

Teaching methods and learning activities

Traditional teaching

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	33,33
Participação presencial	0,01
Trabalho escrito	66,66
Total:	100,00

Calculation formula of final grade

The final grade is the average of the 2 written essays and the final exam.

Classification improvement

Only the grade of the exam can be improved through a make-up exam.